What are you using the area for? If you are planting ornamentals - perennials, shrubs, trees - did you mulch the area after planting? Here in the hot south, mulch is an essential part of keeping the soil from excessive drying (and cracking) by keeping it cooler and retaining moisture longer.

Mulch choices include pine straw, shredded hardwood, and pine bark chips. Organic mulches like these also degrade over time, adding more organic material to improve the soil (they also attract earthworms and other small bugs that will help improve the soil through their activities). As they degrade, you will have freshen them by adding more mulch.

Building up is always easier than digging amendments in. A lot of stuff will do fine with just a skin of topsoil on top of clay. If you wanted something larger than lawn grass in that area you might have to go up a little higher.

A lot of the clumping/decorative grasses will grow just fine in solid clay.

Whoops I guess I should have clarified, I have a vegetable garden: tomatoes, basil, zucchini, squash, mint, parsley

Next week I am planting for fall: Mustard, spinach and lima beans

TRIANGLEJOHN: "If you wanted something larger you might have to go up a little higher."

Right now I am small, but eventually I do want a full acre garden, what do you mean by this and how could I deal with red clay on such a large scale with out breaking the bank?

No I meant if you were just growing a ground cover or turf you could get away with a thin skin of topsoil on top of your clay. Veggies and herbs probably need about 6-10 inches or more. When you pile it up deep, compost/topsoil always goes away during the summer so you have to add more each year.

If it was me I would work on getting some form of drainage system in place before you invest in more topsoil or compost. Either dig some valleys or put in the french drain type of plastic pipe - nothing that deep just a few inches so that excess rainwater runs off the spot. No garden plants like to sit in wet soil (veggie/herbs). You could just build tall mounds of good soil in long rows or build raised beds, no need to cover the entire area with expensive stuff. A lot of plants will send their roots down into solid clay, but when we get a lot of rain those roots usually rot away. If you can mound up good soil on top of your clay every year, eventually the earth worms will work it all together for you but it takes years.

If you have a quarry nearby, you may also want to have some pea gravel delivered and till in it. Works great to break up the clay soil. Tilling in shredded leaves works good. Also, growing a winter cover crop like clover or rye over the winter and tilling it in Spring works great to improve the tilth of clay soil.

For a veggie plot, mulching with grass clippings or cheap hay (especially if you can get hay mixed with manure from a stable) would be sufficient.

As John said, you want to get critters involved too, so adding these organic materials for them to munch on will help. Over time, it improves.

I grow quite a few vegetables including tomatoes, eggplant, basil, various other herbs, and squash in our NC red clay and have no issues doing so. The secret is mulch which will keep the moisture that you or Mother Nature provides in the soil. Clay is a NC staple unless you live near the coast and NC has always been an agricultural state. Clay holds moisture well, but when it dries out it is diffult to re-wet or takes small quantities over a prolonged period to re-wet. Mulch of any type will help prevent clay from crusting over and being hydrophobic.

the "soil" in my backyard is actually rough filler junk from a construction site (long story). i have a very limited budget so i made four raised beds out of cinder blocks. i bought some lovely topsoil and have a fabulous fruit/veggie garden this year!

As a Master Gardener, I have learned that if you put peat moss in this red clay, it will NOT mix. What will happen is the peat will end up bonding back together causing a barrier so that water cannot move through it, nor can roots penetrate it.
The best amendment for clay is Mulch, Mulch, Mulch. Let it break down and do what nature means for it to do. If you have access to compost, that's the same thing. After years of mulching, I now have nice soil. Also, you might want to do a soil test. You can get the boxes and forms from your local Agriculture center.
The testing is free in NC. One of the last states to do this.